If a mode has one swapped-out neighbor, then there are no errors due to swap-outs as the net effect of a single swap-out after applying the \(CZ\)  gates is a stabilizer.
In this case, the error probability is the probability of incorrectly binning the state [1]}, using the standard binning function and assuming a classical noise channel with parameter \(\tilde{\delta }\) , which we derive from \(\tilde{\Sigma }_p\) .
For \(m\ge 2\) , we derive the weights in eq:errorprob from simulations which we detail in sec:decoderweights.
The weight of the corresponding arc in the decoding graph is then \(-\log w(z, m, \tilde{\delta })\)  [2]}.
